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"You have an obligation when you run a business to maximise the profits and if there is a tax law that says I can deduct this, you deduct it," Mr Giuliani told ABC News, suggesting investors in Mr Trump's company probably would have sued him had he done otherwise.

"If everybody in this country was a 'genius,'" the Vermont senator told ABC, "we would not have a country".

While not admitting to paying little or nothing in taxes, Mr Trump boasted on Twitter that what he called his deftness in fiscal and business dealings is one of his greatest strengths.

"I know our complex tax laws better than anyone who has ever run for president and am the only one who can fix them," he wrote after The Times story appeared.

The real estate mogul declared a loss of nearly US$1 billion on his 1995 income tax return, enabling him to legally avoid paying taxes for almost two decades, according to documents obtained by the New York Times.

He has repeatedly refused to make his tax filings public, the first major party presidential contender to do so since Richard Nixon in the 1970s.

Mr Trump has said he will release his tax returns only after the federal authorities complete an ongoing audit.

However, tax officials - without confirming or denying that Mr Trump's tax filings are under review - have said being under audit does not prevent their release.

A lawyer for Mr Trump said publication of Mr Trump's tax returns is illegal because he did not authorise it, and threatened "appropriate legal action" against The Times, the paper reported.

During last week's acrimonious first presidential debate, Mrs Clinton suggested that Mr Trump is hiding "something terrible" by failing to produce his tax returns.

"Maybe he doesn't want the American people, all of you watching tonight, to know that he's paid nothing in federal taxes," she said during Monday night's debate.

She prompted this Mr Trump retort: "That makes me smart." Numerous reports have suggested he has used high-pressure tactics to convince officials in New York and elsewhere to give him tax breaks and other hugely favourable conditions in his deals.

He is also reported to have taken massive, albeit legal, tax breaks on failing businesses, earning a fortune while shareholders and investors swallowed large losses and contractors went unpaid.

"Despite losing a billion dollars, Mr Trump wants to reward himself with more tax breaks on inherited wealth while stiffing middle-class families who earn their paychecks with hard work," he said in a statement.

Mr Reid added that Americans "deserve to know who has leverage over this man who wants to be president."

"Mr Trump has had a really bad week: He failed in the debate," he said in an interview with barely suppressed glee.

"He has spun out of control subsequent to that. Insulting (Venezuela-born beauty queen Alicia) Machado. His 3 am tweet storm," he added, recounting other Trump controversies that dominated headlines last week.

"You know, his campaign is spinning out."

In the latest poll showing a boost for a newly energised Mrs Clinton this week, an ABC News/Washington Post survey released on Sunday said 53 per cent of Americans saw Mrs Clinton as the winner, compared to 18 per cent for Mr Trump.

Nearly half of respondents said he got facts wrong during the debate and a third that he lied outright, while his unpopularity rating grew to 64 per cent in the same poll, compared to 53 per cent for Mrs Clinton.

Mr Trump spent most of last week embroiled in controversy over his abusive comments about Ms Machado, who won the Miss Universe pageant - owned by Mr Trump at the time - in 1996.

He doubled down this week, including in his predawn Twitter rant Friday with more insults about Ms Machado - a tirade Mrs Clinton said proves he is "temperamentally unfit" for the presidency.

Mr Trump went on the attack again on Saturday, mocking the former first lady for a recent bout with pneumonia and raising questions about her loyalty to her husband, former president Bill Clinton.

His running mate Mike Pence is set to debate his Democratic counterpart Tim Kaine on Tuesday. But Americans are expected to pay scant attention, with the focus firmly on Mr Trump with little more than a month to go before the November 8 election.